An inhomogeneous Weibull–Hawkes process to model underdispersed acoustic cues
Funding: TAM time covered by ACCURATE, funded by the US Navy Living Marine Resources program (contract no. N3943019C2176). TAM thanks partial support by CEAUL (funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal, through the project UIDB/00006/2020). This work was supported by Marsden F...
Published in: | Journal of Agricultural, Biological and Environmental Statistics |
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Online Access: | https://hdl.handle.net/10023/29870 https://doi.org/10.1007/s13253-024-00626-w |
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ftstandrewserep:oai:research-repository.st-andrews.ac.uk:10023/29870 2024-09-09T20:10:23+00:00 An inhomogeneous Weibull–Hawkes process to model underdispersed acoustic cues Van Helsdingen, Alec B.M. Marques, Tiago A. Jones-Todd, Charlotte M. University of St Andrews.School of Mathematics and Statistics University of St Andrews.Centre for Research into Ecological & Environmental Modelling University of St Andrews.Statistics 2024-05-13T11:30:13Z 24 1463438 application/pdf https://hdl.handle.net/10023/29870 https://doi.org/10.1007/s13253-024-00626-w eng eng Journal of Agricultural, Biological and Environmental Statistics 302081018 57bf9d9e-1c19-446d-b141-d5804e45bf00 85192808387 Van Helsdingen , A B M , Marques , T A & Jones-Todd , C M 2024 , ' An inhomogeneous Weibull–Hawkes process to model underdispersed acoustic cues ' , Journal of Agricultural, Biological and Environmental Statistics , vol. Early View . https://doi.org/10.1007/s13253-024-00626-w 1537-2693 RIS: urn:F8C64066510CEC61E36E499BF81DB1C6 RIS: Van Helsdingen2024 ORCID: /0000-0002-2581-1972/work/159882869 https://hdl.handle.net/10023/29870 doi:10.1007/s13253-024-00626-w Copyright © 2024 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Overdispersion Point patterns Self-excitement Sperm whale Underdispersion Statistics and Probability General Environmental Science Agricultural and Biological Sciences (miscellaneous) General Agricultural and Biological Sciences Statistics Probability and Uncertainty Applied Mathematics DAS Journal article 2024 ftstandrewserep https://doi.org/10.1007/s13253-024-00626-w 2024-08-28T00:12:18Z Funding: TAM time covered by ACCURATE, funded by the US Navy Living Marine Resources program (contract no. N3943019C2176). TAM thanks partial support by CEAUL (funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal, through the project UIDB/00006/2020). This work was supported by Marsden Fund proposal UOA 3723517 and Asian Office of Aerospace Research & Development grant FA2386-21-1-4028. A Hawkes point process describes self-exciting behaviour where event arrivals are triggered by historic events. These models are increasingly becoming a popular choice in analysing event-type data. Like all other inhomogeneous Poisson point processes, the waiting time between events in a Hawkes process is derived from an exponential distribution with mean one. However, as with many ecological and environmental data, this is an unrealistic assumption. We, therefore, extend and generalise the Hawkes process to account for potential under- or overdispersion in the waiting times between events by assuming the Weibull distribution as the foundation of the waiting times. We apply this model to the acoustic cue production times of sperm whales and show that our Weibull–Hawkes model better captures the inherent underdispersion in the interarrival times of echolocation clicks emitted by these whales. Peer reviewed Article in Journal/Newspaper Sperm whale University of St Andrews: Digital Research Repository Hawkes ENVELOPE(167.700,167.700,-73.533,-73.533) Hawkes Point ENVELOPE(-101.919,-101.919,73.085,73.085) Marsden ENVELOPE(66.067,66.067,-67.867,-67.867) Journal of Agricultural, Biological and Environmental Statistics |
institution |
Open Polar |
collection |
University of St Andrews: Digital Research Repository |
op_collection_id |
ftstandrewserep |
language |
English |
topic |
Overdispersion Point patterns Self-excitement Sperm whale Underdispersion Statistics and Probability General Environmental Science Agricultural and Biological Sciences (miscellaneous) General Agricultural and Biological Sciences Statistics Probability and Uncertainty Applied Mathematics DAS |
spellingShingle |
Overdispersion Point patterns Self-excitement Sperm whale Underdispersion Statistics and Probability General Environmental Science Agricultural and Biological Sciences (miscellaneous) General Agricultural and Biological Sciences Statistics Probability and Uncertainty Applied Mathematics DAS Van Helsdingen, Alec B.M. Marques, Tiago A. Jones-Todd, Charlotte M. An inhomogeneous Weibull–Hawkes process to model underdispersed acoustic cues |
topic_facet |
Overdispersion Point patterns Self-excitement Sperm whale Underdispersion Statistics and Probability General Environmental Science Agricultural and Biological Sciences (miscellaneous) General Agricultural and Biological Sciences Statistics Probability and Uncertainty Applied Mathematics DAS |
description |
Funding: TAM time covered by ACCURATE, funded by the US Navy Living Marine Resources program (contract no. N3943019C2176). TAM thanks partial support by CEAUL (funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal, through the project UIDB/00006/2020). This work was supported by Marsden Fund proposal UOA 3723517 and Asian Office of Aerospace Research & Development grant FA2386-21-1-4028. A Hawkes point process describes self-exciting behaviour where event arrivals are triggered by historic events. These models are increasingly becoming a popular choice in analysing event-type data. Like all other inhomogeneous Poisson point processes, the waiting time between events in a Hawkes process is derived from an exponential distribution with mean one. However, as with many ecological and environmental data, this is an unrealistic assumption. We, therefore, extend and generalise the Hawkes process to account for potential under- or overdispersion in the waiting times between events by assuming the Weibull distribution as the foundation of the waiting times. We apply this model to the acoustic cue production times of sperm whales and show that our Weibull–Hawkes model better captures the inherent underdispersion in the interarrival times of echolocation clicks emitted by these whales. Peer reviewed |
author2 |
University of St Andrews.School of Mathematics and Statistics University of St Andrews.Centre for Research into Ecological & Environmental Modelling University of St Andrews.Statistics |
format |
Article in Journal/Newspaper |
author |
Van Helsdingen, Alec B.M. Marques, Tiago A. Jones-Todd, Charlotte M. |
author_facet |
Van Helsdingen, Alec B.M. Marques, Tiago A. Jones-Todd, Charlotte M. |
author_sort |
Van Helsdingen, Alec B.M. |
title |
An inhomogeneous Weibull–Hawkes process to model underdispersed acoustic cues |
title_short |
An inhomogeneous Weibull–Hawkes process to model underdispersed acoustic cues |
title_full |
An inhomogeneous Weibull–Hawkes process to model underdispersed acoustic cues |
title_fullStr |
An inhomogeneous Weibull–Hawkes process to model underdispersed acoustic cues |
title_full_unstemmed |
An inhomogeneous Weibull–Hawkes process to model underdispersed acoustic cues |
title_sort |
inhomogeneous weibull–hawkes process to model underdispersed acoustic cues |
publishDate |
2024 |
url |
https://hdl.handle.net/10023/29870 https://doi.org/10.1007/s13253-024-00626-w |
long_lat |
ENVELOPE(167.700,167.700,-73.533,-73.533) ENVELOPE(-101.919,-101.919,73.085,73.085) ENVELOPE(66.067,66.067,-67.867,-67.867) |
geographic |
Hawkes Hawkes Point Marsden |
geographic_facet |
Hawkes Hawkes Point Marsden |
genre |
Sperm whale |
genre_facet |
Sperm whale |
op_relation |
Journal of Agricultural, Biological and Environmental Statistics 302081018 57bf9d9e-1c19-446d-b141-d5804e45bf00 85192808387 Van Helsdingen , A B M , Marques , T A & Jones-Todd , C M 2024 , ' An inhomogeneous Weibull–Hawkes process to model underdispersed acoustic cues ' , Journal of Agricultural, Biological and Environmental Statistics , vol. Early View . https://doi.org/10.1007/s13253-024-00626-w 1537-2693 RIS: urn:F8C64066510CEC61E36E499BF81DB1C6 RIS: Van Helsdingen2024 ORCID: /0000-0002-2581-1972/work/159882869 https://hdl.handle.net/10023/29870 doi:10.1007/s13253-024-00626-w |
op_rights |
Copyright © 2024 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
op_doi |
https://doi.org/10.1007/s13253-024-00626-w |
container_title |
Journal of Agricultural, Biological and Environmental Statistics |
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1809944788816887808 |